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We study a class of feedback oscillators realized by a phase-insensitive amplifier in positive feedback, where either the amplifier or the feedback element may determine the oscillator's linewidth. The spectral purity of the output of such a device originates from basic demands of quantum mechanics and causality. The resulting expression generalizes the Schawlow-Townes limit, which is itself one component of a standard quantum limit for feedback oscillators. Recently realized bad-cavity oscillators, such as superradiant lasers and solid-state masers, can saturate this generalized Schawlow-Townes limit. This limit can be surpassed through appropriate quantum engineering, for example, by atomic spin squeezing in a superradiant laser.
Loughlin et al. (Mon,) studied this question.